Kolmogorov complexity is very often defined for bitstrings. The complexity of a positive integer n is typically defined by the complexity of the string containing n zeros. (But here, any computable injective function from integers to strings could be chosen.)

Infact I'm confused with the expression "information content" of a word x as a information carrier and measuring this information content by K(x), the Kolmogorov complexity of x. I want to know why a word x with a large complexity has high "information content" and vice versa?

K(x) represents the shortest program that prints the string on a universal turing machine (say computer). You can compare it a bit to the effort needed to memorize some text. A text which where each letter was randomly generated, is hard to memorize, and has large complexity. On the other hand, memorizing a full page containing only blancs is easy, and it can been be printed by a short program. On the other hand, Of coarse a randomly generated text has no useful information, the notion useful information is subjective. (Although some attempts for mathematical definition of an objective notion exist too, it is called algorithmic minimal sufficient statistic.)

A text which where each letter was randomly generated, is hard to memorize, and has large complexity. Does it mean that this text has high (maybe no useful) information content ? Please let me ask my question in another form: Let x and y be binary words of the same length and K(x) > K(y). Does it mean that the information content of x is greater than the information content of y and what does this "information content" really mean?

By definition, K(x) is the minimal length of a program that prints x. If K(x) > K(y) it means that a shortest program for x has larger length than a shortest program for y. Whatever it means is philosophy. There less than 2^n strings x with complexity K(x) < n, because there are 2^0 + 2^1 + ... + 2^{n-1} = 2^n - 1 binary programs of length less than n. Thus, most strings of length n have complexity close to n, and this is why random strings have large information (unless an unlikely event has occurred in the generation process).